[matches/honours.git] / thesis / thesis.tex

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%\title{\bf Characterisation of nanostructured thin films}
%\author{Sam Moore\\ School of Physics, University of Western Australia}
%\date{April 2012}
%\maketitle

\begin{center}
        B.Sc. (Hons) Physics Project \par
        {\bf \Large Thesis} \par
        Samuel Moore \\
        School of Physics, University of Western Australia \\
        April 2012
\end{center}
\section*{Characterisation of Nanostructured Thin Films}
{\bf \emph{Keywords:}} surface plasmons, nanostructures, spectroscopy, metallic-blacks \\
{\bf \emph{Supervisers:}} W/Prof. James Williams (UWA), Prof. Sergey Samarin (UWA) \\

\pagebreak
\tableofcontents

\pagebreak

\section*{Acknowledgements}

I am extremely grateful for the support offered to me by many individuals during this project. Thanks to my supervisors Prof Sergey Samarin and W/Prof Jim Williams for envisioning the project, and their invaluable support throughout the year. I would also like to thank staff members at CAMSP for assisting with the supervision of this project. In particular I am extremely grateful for the help and advice given by Dr Paul Gualiardo during the construction and testing of the Total Current Spectroscopy experiment.

Thanks to Alexie ??? from CMCA for producing the SEM images which proved a valuable aid for understanding the structure of metallic-black films.

I would also like to endorse the team at J.A Woolam, who provided replacement pins for the ellipsometer alignment detector at no charge after one of the original pins became mysteriously damaged.

Congratulations and thanks to Jeremy Hughes who successfully predicted that the emission current of the electron gun was varying sinusoidally due to the changing temperature of the room. Commisserations to Alexander Mazur, whose suspicians that the vacuum chamber contained a pulsar proved wrong.

Finally, thanks to all my family and friends for their support and for continuing to put up with my slow descent into madness during the last 12 months. 

\section{Introduction}

The report will be organised as follows; first we will discuss literature relating to surface science and nanostructured thin films in particular. We will then give an overview of the primary experimental techniques employed during this project, before presenting experimental results. Finally, we will discuss stuff.

\section{Overview}

In this section we provide an overview of theoretical and experimental literature related to the properties of nanostructured thin films. We also include a summary of the past research which focuses on metallic-black films.

\subsection{Electron Structure of Bulk and Surface}


\subsection{Plasmons}


\subsection{Metallic-Black Films}

So called ``Metallic-Black'' films are the result of deposition of metal elements at high pressure (of the order of $10^{-2}$ mbar). The films are named due to their high absorbance at visible wavelengths; they appear ``black''. There is a remarkable contrast between such films and films deposited under ultra-high vacuum, which are typically highly reflective, exhibiting similar optical properties to a bulk sample of the metal.

This phenomenom has been known since the early 20th century, with the first papers on the subject published by Pfund in the 1930s \cite{pfund}. Pfund's research has been mostly qualitative, and estabilishes the conditions for formation of metallic black films for a number of different metal elements. More extensive research has been carried out on the structural and optical properties of these films by Louis Harris and others from the 1950s until the 1970s \cite{}. Despite advances in computer technology revolutionising the field of surface science, little work has been done since Harris' contributions. %TODO: Check for any recent work

Secondary Electron Microscope (SEM) images of Au deposited on Si at high and low pressures were produced at the Centre for Microscopy Characterisation and Analysis (CMCA), UWA. These images are similar to previous images produced by Harris \cite{}. The film imaged on the left (high pressure) appears black at visible wavelengths, whilst the film on the right (low pressure) appears golden yellow.

%TODO: Insert images

\begin{center}


\begin{tabular}{cc}
        \includegraphics[scale=0.2]{figures/Au_BLACK_200nm.png} & %\captionof{figure}{Au-Black SEM Image} \label{Au_BLACK_200nm.png} &
        \includegraphics[scale=0.2]{figures/Au_semi-shiny_1_SEM.png} %\captionof{figure}{Au SEM Image} \label{Au_semi-shiny_1_SEM.png}          
        

\end{tabular}

        \captionof{figure}{{\bf SEM images of Au deposited on Si at $2\times10^{-2}$mbar (left) and $1\times10^{-6}$mbar.} Note that the scales are very similar for both images.}              

\end{center}

The structural difference between the two films is striking, and yet the exact mechanism behind the formation of the metallic-black film remains unclear. 
% TODO: Attempt to find explanation of structure

Nanostructured metal films prepared at low pressure are often approximated by an isotropic layer of spherical blobs upon the substrate, or even as a uniform layer with an ``effective'' thickness \cite{}. As the right image in Figure \ref{} shows, this is largely representative of the structure of such a film. In contrast, the metallic-black film appears non-uniform; as a result more complicated models are required to theoretically describe the properties of metallic-black films.

Harris et al. have produced experimental results of the transmission of metallic-black films from visible wavelengths to the far-infrared \cite{}. By modelling the film as a layer of metallic strands, acting as ``condensors'', Harris et al. arrived at an expression for the electron relaxation time of [element]-black \cite{}, leading to a a transmission spectrum in good agreement with experimental results.


More recently, it has been suggested that metallic-black films may exhibit plasmonic properties that could be exploited to increase the efficiency of thin film solar cells \cite{pandjwani}. In this work, the author shows that 

However, currently there is no direct evidence of plasmon excitations in metallic-black films. %TODO: Check for evidence of plasmonic behaviour in metallic-black films

\begin{center}
        \includegraphics[scale=0.2]{figures/300V-01.jpg}
        \captionof{figure}{{\bf Au-black film viewed at magnifications of x20000, x50000, x100000 and x200000} (top left, top right, bottom left, bottom right). The film appears non-isotropic, and possibly fractal like upon magnification. This structure has lead some reasearchers to  refer to the deposited films as ``smokes'' \cite{}.}
        \label{300V-01.jpg}
\end{center}

\pagebreak

\section{Experimental Techniques}

\subsection{Secondary Electron Spectroscopy}

Secondary Electron Spectroscopy encompasses a large group of techniques used for studying the electron spectra of surfaces and solids. In these methods a beam of primary electrons is directed at a surface. The interactions between primary electrons and the surface give rise to an energy distribution of electrons elastically and inelastically scattered from the surface. Analysis of the distribution of the scattered ``secondary'' electrons gives information about the electron energy spectrum of the target surface.


\begin{center}
        \includegraphics[scale=0.40]{figures/se_dist.pdf}
        \captionof{figure}{{\bf Model of Secondary Electron Distribution}}
        \label{se_dist.pdf}
\end{center}

Figure \ref{se_dist.pdf} shows the general shape of the secondary electron distribution for a primary electron energy of $E_p$. The narrow peak centred at $E = E_p$ is due to elastically scattered electrons; the width of this peak is determined by the distribution of primary electron energies, as well as the resolution of the detector. The broad peak in the low energy part of the spectrum is due to inelastically scattered electrons. The thick curve shows 

Real secondary electron distributions also show fine structure imposed upon the inelastic part of simplified spectrum described above. This fine structure is characteristic of the target surface. Near to the elastic peak, fine structure is caused by energy loss to interband transitions and plasma vibration excitation. The central part of the distribution contains fine structure due to Auger electron emission, and energy losses due to excitation of inner electrons. Fine structure at low energies is due to the structure of empty states of the solid.

Techniques of Secondary Electron Spectroscopy can be divided into two classes. Energy-resolved methods are based upon observation of the secondary electron distribution at a fixed primary electron energy. These methods aim to examine specific secondary emission processes which occur within a selected energy interval. In contrast to Energy-resolved methods, Total Current (or Yield) methods measure the total current of secondary electrons as a function of primary electron energy. 

The focus of this project has been low energy Total Current Spectroscopy (TCS). While Total Current methods provide less detailed information about secondary emission processes within a solid, they are useful for characterisation of the electron structure. Total Current methods are also simpler to realise experimentally, as they do not require energy analysers, and current measurement may be performed external to the vacuum chamber.


\subsection{Total Current Spectroscopy}

Figure \ref{} shows a simplified schematic for the Total Current Spectroscopy experiments conducted during this study. An electron gun is used to produce the beam of primary electrons. Electrons are emitted from a cathode held at negative potential relative to the target. These electrons are focused into a beam and accelerated onto the target through the electric field produced by a series of electrodes. A detector is used to measure the total current passing through the target.


A major advantage of Total Current Spectroscopy methods is the relative simplicity of the experimental setup. Because energy resolution of secondary electrons is not required, current measurement can be performed external to the vacuum chamber, using a conventional ammeter.

If the current incident upon the sample is $I_{\text{total}}$, and the current of secondary electrons scattered from the surface is $I_r$, then the transmitted current $I_t$ is given by:

\begin{align*}
        I_t &= I_{\text{total}} - I_r
\end{align*}

Generally $I_{\text{total}}$ is assumed to be independent of initial energy $E$. This assumption is valid if the initial energy is small compared to the accelerating potential of the gun, and the distance of the sample from the gun is sufficiently large.

In this case, differentiating with respect to $E$:
\begin{align*}
        \der{I_t}{E} &= - \der{I_r}{E}
\end{align*}

Figure \ref{} is a block diagram of the experimental setup including measurement and control systems external to the vacuum chamber.

\subsubsection{Electron Optics}

The electron gun used for this experiment was repurposed from an old Cathode-Ray Oscilloscope (CRO). Figure \ref{} shows a simplified diagram of the electron gun, whilst Figure \ref{} shows a photograph of the gun. 

The full circuit diagram for the electron gun control circuit is shown in Appendix A. \cite{}

\subsubsection{Automatic Data Acquisition}

In order to collect data on the large number of planned samples for the study, some form of automation was required. The automated system needed to be able to set the initial energy by adjusting the potential of the cathode relative to the sample, and simultaneously record the total current through the sample.

The available power supplies at CAMSP featured analogue inputs for external control. This meant that a Digital to Analogue Convertor (DAC) card was needed to interface between the control computer and the power supply. In addition, the available instruments for current measurement produced analogue outputs. As a result, Analogue to Digital Convertors (ADCs) were required to automate the recording of total current.

Although an external DAC/ADC box was already available for these purposes, initial tests showed that the ADCs on the box did not function. The decision was made to design and construct a custom DAC/ADC box, rather than wait up to two months for a commercial box to arrive. The design of the custom DAC/ADC box is discussed in detail in Appendix B, and the software written for the on-board microprocessor and the controlling computer are presented in Appendix D.


\subsection{Ellipsometry}

Ellipsometry is an optical technique most commonly used to determine the thickness of multilayered thin films. Ellipsometry can also be used to determine the optical constants and properties of unknown materials. 

Essentially, ellipsometry measures the change in polarisation of light reflected from a surface. This change in polarisation can be related to properties of the surface if knowledge of the surface is correctly applied. For a bulk sample, the change in polarisation can be directly related to the optical constants of the material.

\subsubsection{Description of the Polarisation state of Light}




\subsubsection{Variable Angle Specroscopic Ellipsometry}
A single ellipsometric measurement involves recording $r_p$ and $r_s$ at one angle and wavelength. The earliest ellipsometers were 


A Variable Angle Spectroscopic Ellipsometer at CAMSP has been used to perform a variety of measurements on metallic thin films.,

The VASE

\subsection{Vacuum Techniques and Sample Preparation}

Both the TCS experiments and the deposition of films must be performed in a vacuum. For convenience and simplicity, a single vacuum chamber at CAMSP has been repurposed to perform both of these tasks. The chamber can be pumped by a molecular turbo pump, backed by a rotaray pump, to a base pressure of $2\times10^{-8}$ mbar, or by the rotary pump alone to a base pressure of $1\times10^{-3}$ mbar. The pressure is monitored using either a pirani or ion gauge (for pressures greater than and less than $10^{-3}$ mbar respectively).

%TODO: Insert graphs of pressure in chamber

Figure \ref{} shows a diagram of the vacuum chamber used both for the creation of nanostructured thin films and their study using TCS. A rotatable sample holder is positioned in the centre of the chamber. One flange of the chamber houses the electron gun used for TCS measurements, whilst the opposite flange contains feedthroughs on which tungsten filament evaporators are mounted. This setup allows for almost immediate study of evaporated films by simple rotation of the sample holder to face the gun.


The evaporators consist of a tungsten wire filament attached between two feedthroughs. A piece of a desired metal is folded over the apex of the tungsten wire. The metal can be heated by passing a current through the filament; near the metal's melting point it begins to evaporate. To clean the metal surface and ensure uniform evaporation, this procedure is first performed at low pressure (below $10^{-6}$ mbar) with no sample in the chamber, with the current increased until the metal piece begins to melt and forms a ball on the wire. Figure \ref{} shows an image of an evaporator that has been prepared for use.

This study focused primarily on depositing Au films on an Si substrate, at both high and low pressures. The substrates and sample holders were cleaned in an acetone bath immediately prior to insertion in the vacuum chamber.



\section{Experimental Results and Discussion}
\subsection{TCS Measurements}


\subsection{Ellipsometric Measurements}


\section{Achievements}

\pagebreak

\section*{Appendix A - Electron Gun Control and Current Measurement Circuit}

Figure \ref{} shows the complete electron gun control circuit. The circuit was designed and constructed as part of this project. The design is based upon examples found in \cite{komolov} and \cite{Moore}.

\subsection*{Electron Optics}
The electron gun has been recycled from a Cathode Ray Oscilloscope. Figure \ref{} shows a diagram and photograph of the gun. The gun contains a total of 9 electrodes; several electrodes are held at the same potential, as shown in the figure. From figure \ref{} it can be seen that the electrode potentials are referenced to the initial energy, rather than ground. Because of the relatively large distance between the gun and sample (held at ground), this ensures that changes in initial energy do not significantly effect the focusing properties of the gun.

The optimum potentials of the gun electrodes were determined manually by focusing the gun on an Au film (deposited on Si). I-V curves obtained by measuring current through the sample as a function of initial energy were obtained. The electrode potentials were systematically altered to ensure the curves were as close as possible to the ideal model.

\subsection*{Model of I-V curves}
The current detected through the sample is due to electrons which have sufficient energy to overcome the potential barrier between the surface and vacuum, entering the conduction band



\subsection*{}

The filament is surrounded by a conducting cylindrical electrode commonly called the ``Venault''. The potential of the venault has little effect on the focusing properties of the gun, but is largely responsible for determining the current leaving the gun. Figure \ref{} shows I-V curves for several venault settings, including the optimum setting.

\subsection*{Einzel Lens}

Electrodes passing through the aperture of the venault are accelerated towards the target through six electrodes. The first and last pair of electrodes are at the same potential; the central pair are held at a different potential. Such an arrangement can be considered as an ``Einzel'' or ``zoom'' lens. It can be shown \ref{Moore} that the 

\pagebreak

\section*{Appendix B - DAC/ADC Box - Hardware}

\subsection*{Overview}

In order to automate TCS experiments, both Digital to Analogue and Analogue to Digital Convertors were required (DAC and ADC). To provide these, a custom DAC/ADC Box was designed and constructed. The box can be controlled by any conventional computer with available RS-232 serial communication (COM) ports. Most modern computers no longer feature COM ports; a commercially available convertor can be used to interface between the box's RS-232 output and a standard Universal Serial Bus (USB) port.


The key components of the DAC/ADC box hardware include:

\begin{itemize}
        \item Microprocessor (AVR Butterfly ATMega169)
        \item Four Analogue to Digital Converter (ADC) inputs
        \item Single Digital to Analogue Converter (DAC) output (Microchip MCP4922)
        \item Analogue electronics for amplification at ADC inputs and DAC outputs
        \item Seperate power supply circuitry for Digital and Analogue electronics
        \item RS-232 communications for control by a conventional PC or laptop
\end{itemize}

\subsection*{Microprocessor}
The DAC/ADC box has been based upon Atmel's AVR Butterfly; an inexpensive and simple demonstration board for the ATMega169 16 Bit microprocessor. The features of the AVR Butterfly include easily accessible ports for Analogue to Digital Convertor (ADC) inputs and digital input/output, an onboard Universal Asynchronous Reciever/Transmitter (USART) for RS-232 serial communications, and a 6 character Liquid Crystal Display (LCD). The AVR Butterfly can be programmed using a conventional computer over the USART using a RS-232 COM port. For modern computers (which do not usually posess COM ports), a RS-232 to USB converter may be used.

Figure \ref{avr_butterfly.pdf} is a labelled photograph of the AVR Butterfly showing the use of the available ports for this project.


%Figure of Butterfly
\begin{center}
  \includegraphics[scale=0.70]{figures/avr_butterfly.pdf}
        \captionof{figure}{AVR Butterfly} \label{avr_butterfly.pdf}
\end{center}

Unless otherwise stated, all voltage differences are specified relative to the power supply ground of the AVR Butterfly.

\subsection*{ADC Inputs}

The AVR Butterfly offers easy access to four of the ATMega169's ADCs through PORTF. Each ADC is capable of measuring voltages of $0 < V_{\text{adc}} < V_{cc}$ with 10 Bit resolution. For measuring voltages outside this range, some circuitry is required between the input voltage and the ADC input. In addition, it is desirable to provide the ADC with some form of input protection against accidental overloading.  Figure \ref{adc_normal.pdf} shows the input circuit which was used for three of the four available ADCs. 

\begin{center}
        \includegraphics[scale=0.50]{figures/adc_normal.pdf}
        \captionof{figure}{ADC4,6,7 Input} \label{adc_normal.pdf}
\end{center}


For making voltage measurements above $V_{cc}$, a voltage divider allows reduction of the voltage at the ADC. By constructing the voltage divider using a variable resistor, the range of measurable inputs could be manually adjusted. 

The diodes shown in Figure \ref{adc_normal.pdf} ensure that the ADC is protected from accidental exposure to voltages outside the acceptable range. In normal operation both diodes are off. If $V_{\text{adc}}$ were to become greater than the reference point $V_{cc}$, current would flow between the ADC input and the reference point, acting to reduce $V_{\text{adc}}$ until it reached $V_{cc}$. Similarly, if $V_{\text{adc}}$ fell below ground, current would flow from ground to the ADC input, acting to increase $V_{\text{adc}}$ until it reached ground.

The voltage at the ADC input can be related to the input of the voltage divider using Kirchoff's Voltage Law and Ohm's Law:
\begin{align*}
 V_{\text{adc}} &= \frac{R_1}{R_1 + R_2} V_{\text{in}}
\end{align*}
Where $V_{\text{in}}$ is the voltage at the input of the circuit, $R_1$ is a fixed resistor, and $R_2$ is variable resistor.

$V_{\text{in}}$ can be therefore be determined from the registered ADC counts by:
\begin{align*}
        V_{\text{in}} &= \left(\frac{\text{ADC counts}}{2^{10}}\right) \times \frac{R_1 + R_2}{R_1} V_{cc}
\end{align*}

\subsubsection*{Differential ADC Input}

During the testing of the TCS experimental apparatus, it became desirable to measure the emission current of the electron gun. The electrometer used for this current measurement was capable of producing an analogue output in the range of $0-1V$. However, the negative terminal of this output was not at ground potential, but rather at the same terminal as the negative input terminal. Directly connecting the electrometer output to one of the ADC inputs discussed above would create a short circuit between the initial energy power supply, and ground (refer to Figures \ref{} and \ref{}). Therefore, it was decided to add a differential stage before the input of one of the ADCs.

Figure \ref{adc5.pdf} shows the modification made to the input for ADC5 on the AVR Butterfly. The original voltage divider and input protection discussed above are still present. The modifications include the addition of an instrumentation amplifier, and low pass filters.

\begin{center}
        \includegraphics[scale=0.70]{figures/adc5}
        \captionof{figure}{Differential Input stage for ADC5}
        \label{adc5.pdf}
\end{center}

asdfa
The instrumentation amplifier consists of two stages of operational amplifiers (op-amps); input buffers, and a difference amplifier.
The difference amplifier can be shown using the ideal op-amp model to produce an output voltage proportional to the difference between its inputs:

\begin{align*}
        V_{out} &= \frac{R_2}{R_1} \left(V_{2} - V_{1}\right)
\end{align*}

The two op-amps at the inputs to the differential amplifier are unity gain buffers. Although the outputs of the op amps are equal to their inputs, current is prevented from flowing from the circuit under measurement, and is instead drawn from the op amp power supply. 

In principle, two ADC channels could be used to record the positive and negative outputs of the electrometer seperately, with differencing done in software. However this would require modification to the output cable of the electrometer, which may prove inconvenient for future uses.It was decided that the modification of the cable and added complexity of the software required would be more time consuming than differencing the two inputs using the hardware methods described above.

The low pass filters were added to the inputs of ADC5 after it was found that an unacceptable level of AC noise was being output by the electrometer. The level of noise was too high to be filtered in software, for reasons that will be discussed in Appendix D.

\subsection*{Temperature Measurement}

The AVR Butterfly features an onboard thermistor connected to ADC0. Reading ADC0 and applying the formula given in the AVR Butterfly User's Guide \cite{} results in a temperature measurement. This was useful in establishing a link between the changing chamber pressure and the temperature of the laboratory (see Appendix C).

\subsection*{Power Supplies}
Due to the presence of both analogue and digital electronics in the DAC/ADC box, three seperate supply voltages were required:
\begin{enumerate}
        \item Digital logic in the range $3 \to 4.5$V
        \item Positive op-amp supply in the range $10 \to 15$V
        \item Negative op-amp supply in the range $-10 \to -15$V
\end{enumerate}

Circuitry was designed which allowed two seperate single pole power supplies to be used for Digital logic and the op-amps. A dual 0-30V DC power supply has been used for both digital and analogue circuitry.

\subsubsection*{Logic Power Supply}
The AVR Butterfly runs off $3V < V_{cc} < 4.5V$ DC. Since $V_{cc}$ was also used as the reference voltage for the ADCs and DAC output, it was desirable that $V_{cc}$ be kept constant, despite the absolute level of the power supply. A $3.3V$ voltage regulator has been used for this purpose. The capacitor further smooths the output by shorting high frequency fluctuations to ground.

When the DAC/ADC box was first constructed $V_{cc}$ was supplied by three $1.5V$ batteries. However, due to higher than expected power usage, and the unreliability of the voltage regulator as the input voltage fell below $4V$, inputs for an external power supply were later added.

\begin{center}
        \includegraphics[scale=0.70]{figures/logic_ps}
        \captionof{figure}{Logic Power Supply}
        \label{logic_ps.pdf}
\end{center}

\subsubsection*{Op-amp Power Supply}
The DAC/ADC box circuitry involves several operational amplifiers (LF356), which require dual $\pm 10-15V$ supplies. As there were no dual $\pm$ power supplies available, a single $30V$ power supply was used, with the circuit shown in figure \ref{} used to produce $\pm 15V$ relative to ground.

The buffer amplifier ensures that negligable current can flow from the power supply into the logic and ADC circuits, whilst the capacitor removes high frequency fluctuations of the power supply relative to ground.

\subsection*{DAC Output}
A commercial DAC board was used to produce the DAC output. The Microchip MCP4922 ET-Mini DAC is controlled by the AVR Butterfly using Motorola's Serial Peripheral Interface (SPI) Bus. The software used to implement SPI between the MCP4922 and the AVR Butterfly is discussed in Appendix D.

The ET-Mini DAC can only be powered off $3V$ to $5V$. Using $V_{cc} = 3.3V$ means that the DAC output cannot exceed $V_{cc} = 3.3V$. For TCS, energies of up to $15eV$ are required, so amplification of the DAC output was clearly necessary. A simple non-inverting amplifier with a manually adjustable gain was used to amplify the DAC output by a factor of three. This output was then used to control a laboratory power supply to produce the full range of initial energies.

\subsection*{RS-232 Communications}

The AVR Butterfly features an onboard USART, which can be used both for programming and communication with the ATMega169 processor. The RS-232 communications requires only three wires; Recieve (RX), Transmit (TX) and a common ground. 

The requirement that the AVR Butterfly share a common ground with the controlling computer lead to increased noise through ground loops. This is discussed in more detail in Appendix D.

Although the RS-232 is relatively simple to implement, which makes it ideal for non-proprietry microprocessor applications, most modern computers no longer feature RS-232 COM ports. Although a computer with COM ports was available at CAMSP, due to the extreme unreliability of this computer, it was quickly replaced with a laptop that did not possess COM ports, and a commercial RS-232 to USB converter was used to interface with the laptop.



\section*{Appendix C - Pressure Monitoring}

The pressure in the chamber was monitored by a ion gauge at low pressure (below $10^{-3}$ mbar), and a pirani gauge at high pressure. The gauge included a flurescent Liquid Crystal Display (LCD). In order to automate monitoring of pressure, a USB webcam was placed in front of the gauge LCD. Software was written using the Python Imaging Library (PIL) to convert the image produced by the webcam into a pressure reading. In this way, the pressure could be recorded as a function of time, independent from other measurements performed using the ADC/DAC control box.

Figures \ref{pressure_a.jpg} to \ref{pressure_c.jpg} show the process by which an image taken with the webcam was converted into a pressure reading. The software first identifies bounding rectangles for each individual digit. These are then further subdivided into 7 segments. If enough pixels in a given segment match the colour LCD segments, then the segment can be identified as activated. The software then creates a string corresponding to the activated segments, and looks up the digit in a dictionary.

\begin{center}
        \includegraphics[scale=0.50]{figures/pressure_a.jpg}
        \captionof{figure}{An unprocessed image}
        \label{pressure_a.jpg}
\end{center}

\begin{center}
        \includegraphics[scale=0.50]{figures/pressure_c.jpg}
        \captionof{figure}{Individual digits identified}
        \label{pressure_b.jpg}
\end{center}

\begin{center}
        \includegraphics[scale=0.50]{figures/pressure_d.jpg}
        \captionof{figure}{Activated segments (green) for a single digit}
        \label{pressure_c.jpg}
\end{center}

\section*{Appendix D - Sources of Error}

GROUND LOOOOOOPS!

\section*{Appendix E - Software}

No really, you don't want to know

\pagebreak
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